Changing the Subject of a Formula: Comprehensive Guide with Worksheet

Changing the Subject of a Formula

  • Changing the subject of a formula is one of the essential skills in algebra, which removes the expressions of a specific variable in favour of others.
  • Whether you’re handling physics equations or financial formulas, having the ability to change the definition of a subject lets you adjust equations to your needs.

In this article, we will discuss:

  1. What is changing the subject of a formula?
  2. How to change the subject of a formula?

Here is one more link to practice a few extra questions: Maths Genie Changing the Subject of a Formula Questions

What is changing the subject of a formula?


  • Rearranging an equation is known as changing the subject, which is the process of highlighting the variable of choice as the most important factor in the equation.
  • This manipulation facilitates in separate and clearer understanding of the behaviour of specific variables in a particular mathematical concept.


  • First, these skills aids in problem solving, giving us the chance to examine the outcomes of individual variables.
  • Shows directly how the relationships between the mathematics are established.

How to change the subject of a formula

  1. Identify the Target Variable:

    • Determine which variable needs to be isolated as the new subject of the formula.
  2. Inverse Operations:

    • Utilize inverse operations to manipulate the equation and isolate the desired variable.
    • Common inverse operations include addition and subtraction, multiplication and division.
  3. Maintain Equality:
    • Perform the same operations on both sides of the equation to keep it balanced.

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Solved Example: 

Question 1: In regards to the quadratic equation ax2 + bx + c = 0 with a, b, and c being constants. Replace the subject of the formula by x to isolate the variable x.


  • Step #1: Indicate the Target Variable

In this case, we aim to isolate the variable x and make it the subject of the quadratic equation.

  • Step #2: Use the Quadratic Formula

The quadratic formula is a useful mean for us to extract x of a quadratic equation of type ax2 + bx + c = 0.

Quadratic Formula

Using this formula, a, b and c are the coefficients of the quadratic equation.

Question 2: Given E = mc2, change the subject to m.


  • Step#1: Indicate the Target Variable: m
  • Step #2: Divide both sides by c2:

m = E/c2

Changing the Subject of a Formula Answers

Exam Tips

Importance of Formula Manipulation:

    • Enhances problem-solving capabilities.
    • Provides us with the ability to understand maths in a more refined manner.

Common Techniques in Changing the Subject:

    • Identifying the target variable.

    • Adjusting the value of the variable opposite while keeping an equation balanced.

Applications Across Disciplines:

    • Physics: The variables separate from the equation of motion or energy, for instance.

    • Finance: Analyzing formulas for compound interest or investment returns.

Practice Questions

Question 1: How can you change the subject of the formula A = ½ bh to find h(height)?

Answer :

Question 2: Rearrange t = w/2 to make w the subject.

Answer :


  • The knowledge of the ways to transform a formula to another type assists people in dealing successfully with difficult mathematical problems.

  • Through this particular ability, the interconnection of all the stated variables is uncovered and thus the necessary insights become available.

  • No matter is the subject of physics or finance, altering the subject is a universal technique that has almost endless applications.

  • Building this skill is necessary therefore by challenging the reader with different problems enhancing comprehension.

Worksheet on Changing the Subject of a Formula

Question 1: Make w the subject of the formula s = w/a

Question 2: Given that x + y = 1 What does y equal?

Question 3: Make d the subject of e = d + 5

Question 4: Rearrange this formula to make c the subject a = c – w